Contrastive learning relies heavily on large-scale negative sampling, posing severe optimization challenges when processing high-dimensional sparse features under forced extreme micro-batch conditions. This paper systematically investigates a potential statistical mechanism underlying training instability and numerical collapse under such constraints. Through the multivariate Delta method and asymptotic analysis, we demonstrate that the finite-sample estimation of the empirical partition function introduces structural gradient perturbations that may become more pronounced as the number of sampled negatives decreases. To overcome this limitation, we formalize a decoupled probabilistic alignment theoretical framework governed by a "global intrinsic semantic threshold". By reformulating the alignment task as additive pairwise Bernoulli modeling, the method removes the dependence on a shared partition function, yielding an unbiased finite-batch estimator of the gradient of its explicitly defined population objective. Comprehensive validations across controlled high-dimensional Monte Carlo simulations and a real-world fMRI visual decoding task substantiate our theoretical claims. Under extreme micro-batch limits, where standard contrastive loss triggers numerical divergence, the decoupled objective suppresses gradient variance by nearly 130-fold and maintains stable convergence. This theoretical framework alleviates the structural dependence of high-performance representation learning on massive batches, providing a robust mathematical foundation for resource-constrained scientific computing.
Citation: Yuxiao Zhao, Runtao Duan, Xiaomin Ying, Guohua Dong. Gradient perturbation and decoupled probabilistic alignment in micro-batch contrastive learning: a theoretical analysis[J]. AIMS Mathematics, 2026, 11(8): 26454-26469. doi: 10.3934/math.20261061
Contrastive learning relies heavily on large-scale negative sampling, posing severe optimization challenges when processing high-dimensional sparse features under forced extreme micro-batch conditions. This paper systematically investigates a potential statistical mechanism underlying training instability and numerical collapse under such constraints. Through the multivariate Delta method and asymptotic analysis, we demonstrate that the finite-sample estimation of the empirical partition function introduces structural gradient perturbations that may become more pronounced as the number of sampled negatives decreases. To overcome this limitation, we formalize a decoupled probabilistic alignment theoretical framework governed by a "global intrinsic semantic threshold". By reformulating the alignment task as additive pairwise Bernoulli modeling, the method removes the dependence on a shared partition function, yielding an unbiased finite-batch estimator of the gradient of its explicitly defined population objective. Comprehensive validations across controlled high-dimensional Monte Carlo simulations and a real-world fMRI visual decoding task substantiate our theoretical claims. Under extreme micro-batch limits, where standard contrastive loss triggers numerical divergence, the decoupled objective suppresses gradient variance by nearly 130-fold and maintains stable convergence. This theoretical framework alleviates the structural dependence of high-performance representation learning on massive batches, providing a robust mathematical foundation for resource-constrained scientific computing.
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Yuxiao Zhao, Runtao Duan, Xiaomin Ying, Guohua Dong. Gradient perturbation and decoupled probabilistic alignment in micro-batch contrastive learning: a theoretical analysis[J]. AIMS Mathematics, 2026, 11(8): 26454-26469. doi: 10.3934/math.20261061
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